Strategic sensor placement on graphs

Mohammad Pirani, Joshua A. Taylor, Bruno Sinopoli

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


This paper studies optimal sensor placement in networked control systems for improving the detectability of cyber–physical attacks. The problem is formulated as a game between an attacker and a detector. The attacker's decision is to select a set of nodes in the network to attack, and the detector's decision is to places sensors on a set of nodes. The detector tries to maximize the detectability of attack signals. The attacker tries to maximize its impact while avoiding detection. We analyze the game using structured systems theory and other graph-theoretic concepts. The equilibrium strategy of the detector determines the optimal locations of the sensors. We study pure and mixed strategies for the case of single attacked–single detected nodes. We extend some of our results to the case of multiple attacked–multiple detected nodes. For the cases where the game does not admit a Nash equilibrium, we discuss the Stackelberg game and give graph-theoretic bounds on the game value. Finally, we discuss the Stackelberg equilibrium strategies for simple graph topologies.

Original languageEnglish (US)
Article number104855
JournalSystems and Control Letters
StatePublished - Feb 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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